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The 29-year-old "Top Chef" contestant, who competed in Season 15, recently revealed she has been given a year to live. Ali appeared on "The Ellen DeGeneres Show" Friday to share her story and become "best friends" with Ellen DeGeneres, crossing two more items off her bucket list.

"Right after filming Top Chef, it was supposed to be one of the most exciting times in my life. [Instead], I was in the hospital because I was newly diagnosed with Ewings Sarcoma," she said. "When I was diagnosed, it was obviously incredibly jarring. It was the biggest shock of my life. But, I knew the only way I was going to beat this was through positivity and rallying people around me."

Ali, who would watch DeGeneres' show while undergoing chemotherapy, added, "I am so looking forward to this next year, because I am surrounded with so much positivity. I'm so lucky to have friends and family like I do. We are going to be taking an entire tour of the world, eating all this absolutely delicious food. I know that's the only way to get through this."

When Ali and DeGeneres finally met face-to-face, the famous foodie recounted what a whirlwind the past few years have been. "Thanks to the fans, I won Fan Favorite...which some people say is better than winning the whole thing," she joked. "So, I have that under my belt. "Top Chef" was absolutely incredible. I made wonderful friends. They've been so supportive through this entire journey." About two months after filming, Ali said she noticed a dull ache in her shoulder. After ignoring it for months, she got an MRI.

"Within four hours, [my doctor] called me on my cell phone. He's like, 'Look, I hate to do this on the phone, but I don't want to waste any time. This could be something very serious. I feel like you should call some family to help you through it, because I'm going to refer you to an oncologist.' After we went to Memorial Sloan Kettering in New York, I got my biopsy--and it came back that it was Ewings Sarcoma."

Ewings Sarcoma is a cancer that most often occurs in and around the bones.

Ali, who received support from host Padma Lakshmi and her fellow contestants, remained hopeful she would ultimately beat the disease. "In July I had clear scans. I was technically cancer-free," she said. But, after moving to L.A., Ali said she noticed a "weird ache" in her left hip. "I had this nagging feeling that something wasn't right. So, we went back to New York, got another PET scan and my doctors sat us down. They were like, 'Look, the cancer is back. It's metastasized. The chemo has not worked,'" she recalled. " I looked at my doctor and I was like, 'Tell me straight. How long do I have?' And he's like, 'A year.' It's a lot. It's crazy, but life is crazy."

DeGeneres said she admired Ali's strength. "This is really hard. It's never fair. Anyone who is dealing with anything, you just think, 'This isn't fair.' But you get to live the way we're all supposed to live," she said. "Who knows what tomorrow brings? You just so happen to have this diagnosis, but we all should be living like that, because none of us know what tomorrow is."

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In the next year, Ali said she plans to visit "so many restaurants" around Europe. "You're obviously invited; so is [Portia de Rossi]," she told DeGeneres, naming France, Italy, South Africa and Spain as her dream destinations. Added Ali, "There's so many things I want to do."

Ali's friends have started a GoFundMe page to help with her travel expenses, and a portion of the donations will also go toward research for Ewing Sarcoma. "We want to be a part of helping with that," an emotional DeGeneres told her. "Our friends at Shutterfly want to make sure you get to do everything you want to do--so they're giving you a check for $50,000 to help you out."